494 Proceedings of the Royal Society of Edinburgh. [Sess. 
Children. 
Number of Times each 
Fraternal Group occurs. 
(a, a). 
(a, b). 
(b, 0- 
( 3 
4 n 
Father (a, a) . . < 4 
2 n 
2 n 
U 
4 n 
( 4 
2 n 
2 n 
Father (a, b) . . 1 8 
n 
2 n 
n 
u 
2 n 
2 n 
n 
4 n 
Father (b, b) . .14 
2 n 
2n 
u 
4 n 
On re-arranging we have each group occurring as in the table. 
Brethren. 
Number of Times 
a Group occurs. 
(a, a). 
(a, b). 
(b, b). 
3 
4 n 
8 
2 n 
2 n 
2 
4 n 
8 
n 
2 n 
n 
8 
... 
2 w 
2n 
3 
... 
An 
So that we can write the correlation table for brothers as follows 
First Brother. 
Second 
Brother. 
(a, a). 
(a, b). 
(b, b). 
(a, a) . 
3’An(An - 1) + 8*2^(2w - 1) 
+ 8 n(n- 1) 
8(4?i 2 + 2?i 2 ) 
8 n 2 
(a, b) . 
8(4n 2 + 2 n 2 ) 
2'An(An- 1) 
+ 2A-2n(2n- 1) 
8(4w 2 + 2n 2 ) 
(b, b) . 
8 n 2 
8(4^ 2 + 2n 2 ) 
3*4w(4w-l) + 8*2w(2n-l) 
8 n(n- 1) 
